It looks like Mama Murphy is a bit of an addict, and her chem of choice is just about anything that will get her good and messed up. You have the option of being an enabler here, or you can just ignore the old lady and go about your business. The benefit will most likely end up somewhere in the middle.
For example, we had some Jet on hand and gave it to Mama Murphy, and she told us of a situation that we would be in during one of the main quests, Fallout 4: Unlucky Valentine. That’s the benefit here - giving Mama Murphy chems can give insight into how to get yourself out of some situations that you might otherwise struggle with. The penalty is that both Sturges and Preston Garvey dislike you helping her get high.
We would advise giving her the Jet and building her chair, but then perhaps letting your Charisma build up and trying to convince her to kick the chems once and for all. Honestly, you don’t need the help in your play through, and if you continue to feed her addiction, Mama Murphy will actually die when you give her the Psycho. If you’re willing to go down that road, however, just know that you must wait eight hours to give her more chems.
Let’s assume you want to go all the way with this quest and get Mama Murphy messed up at every opportunity. Well, finding the chems shouldn’t be that hard as you wander the Commonwealth, but if you’re missing something, you can always take a trip to Diamond City, visiting Chem-I-Care to get what you need. Some of this stuff is extremely expensive, so feel free to read about how you can Earn Infinite Caps and Buy Everything in the Game. If you can’t find what you’re looking for in Diamond City, maybe you should wander down the road to Goodneighbor, or… you know… just not feed old ladies drugs in the first place.
If you want to continue with the Minutemen quests, you can progress forward and read about Fallout 4: Taking Independence, or you can return to USgamer’s Fallout 4 Walkthrough and Guide. We’ll have all of the main story quests, as well as the side quests, and a batch of features that should help you master the game in not time.